An Efﬁcient Addressing Scheme and Its Routing Algorithm for a Large-Scale Wireless Sensor Network

So far, various addressing and routing algorithms have been extensively studied for wireless sensor networks (WSNs), but many of them were limited to cover less than hundreds of sensor nodes. It is largely due to stringent requirements for fully distributed coordination among sensor nodes, leading to the wasteful use of available address space. As there is a growing need for a large-scale WSN, it will be extremely challenging to support more than thousands of nodes, using existing standard bodies. Moreover, it is highly unlikely to change the existing standards, primarily due to backward compatibility issue. In response, we propose an elegant addressing scheme and its routing algorithm. While maintaining the existing address scheme, it tackles the wastage problem and achieves no additional memory storage during a routing. We also present an adaptive routing algorithm for location-aware applications, using our addressing scheme. Through a series of simulations, we prove that our approach can achieve two times lesser routing time than the existing standard in a ZigBee network.


INTRODUCTION
Large-scale events such as disaster relief or rescue efforts require the most effective and highly available communication capabilities.To provide better communication and monitoring capabilities, such applications may be tremendously benefited from the use of self-organizing networks over wireless medium [1].Existing wireless sensor networks (WSNs) such as ZigBee network, however, do not scale well, because many of them have targeted smaller deployments, typically less than hundreds of sensors.Real world deployments identified several limitations in the existing WSNs and reported that certain physical topologies would run out of address space quickly [2].
We recognized that such limitations were closely related with the addressing schemes and the routing methods of WSN standards.To uniquely identify sensor nodes through their addresses in an ad hoc and mesh-style wireless network, standard address schemes such as ZigBee Cskip algorithm [3] utilize available address space sparsely, thus causing significant wastage of address space [2,4,5].In a large-scale WSN, flat routing methods are unsuitable because of their flooding nature for routing path construction [6][7][8].On the other hand, tree-based routing methods, at the expense of robustness, achieve acceptable routing performance because of their low routing overhead [9,10].
In this study, we focus on an efficient address assignment scheme by using n-dimensional address subspacing and its tree-based routing algorithm for a large-scale WSN.Especially, we are interested in tackling the address wastage problem for a ZigBee network.We also present a locationaware routing algorithm that also uses our address subspacing and discuss its pros and cons.
This article is organized as follows.In Section 2, various addressing assignment schemes and their routing algorithms are presented.Section 3 introduces the addressing scheme and its routing policy of early ZigBee standard, addresses its problem, and reports several proposals to cope with the problem.In Section 4, we describe our n-dimensional addressing scheme and its routing algorithm that reuses the existing address scheme.In the same section, we also discuss the potential of the location-aware routing algorithm that is also newly devised to improve wireless performance.Section 5 reports the evaluation results of existing addressing scheme and our scheme through simulations.Finally, we describe our contributions and future research direction in Section 6.

RELATED WORKS
Addressing and routing have been extensively studied in the literature for decades.It will be too ambitious to cover all the issues in rather a short section.Instead, we present general ideas and trends in these areas for WSNs.For a better presentation, we separate issues into two parts: addressing and routing.

Addressing
Existing addressing policies in WSNs fall into two groups: tree based and ad hoc based.The tree-based addressing uses hierarchical addressing policy [11,12], while the ad hoc addressing is originated from the addressing schemes for wireless ad hoc network [13][14][15].
PalChaudhuri et al. proposed a robust, stateless addressing, and routing architecture called TreeCast [11].Unlike what the name implies, its address assignment is the most crucial step, while its routing procedure is trivial.It is because the address of a newly joining node is determined on demand and the address in itself encapsulates the path to a parent.Therefore, routing from a source to a sink becomes trivial.A new node joins the network by choosing its parent among candidate parents randomly.Its new address is incrementally allocated by combining the parent address with a locally unique identifier.However, its addressing scheme is only optimized for a single sink node.To support multiple sink nodes, the algorithm requires multiple addresses per node, each of which is originated from individual sink node.Thus, it is useless for the applications that use end-to-end communication between two arbitrary nodes.
Huynh and Hong suggested a hybrid architecture that has both hierarchical and mesh-style routing features [12].Firstly, it is a layered architecture.Every sensor node should reside in one of the layers and needs a unique parent in its above layer, maintaining a hierarchical structure.Once a parent node is chosen, TreeCast-like incremental address assignment is applied, that is, the address of a newly joined node includes its parent address.Therefore, a node in a higher layer always has a smaller address length than other node in a lower layer.Secondly, every node residing in the same layer is interconnected with each other in the form of a de Bruijn graph, a special case of mesh structure.Therefore, if a source and a destination have the same address length, intralayer routing along mesh topology will be performed.Otherwise, interlayer routing along tree topology would then be firstly executed.While it allows arbitrary end-toend communication, its applicability is limited to indoor applications, where all sensor nodes are immovable.
The naive address assignment policy is to use a centralized scheme, where a single server in a network is dedicated to assign addresses for a new node with no conflict.As long as the server operates, uniqueness of allocated addresses is guaranteed.In spite of its simple design, a single-point-offailure problem has been the biggest obstacle in its popular use in ad hoc environments.In a decentralized addressing scheme, each node configures its address and then announces the address through flooding mechanism [13].If any address conflict is detected, all the other nodes in the network will negotiate to resolve the address conflict to validate the uniqueness of the address through global agreement.
IPAA [14] adopts a trial and error policy to find an available IP address for a new node [14].A new node selects two random IP addresses from the IP address block, which is divided into two categories, a temporary address for duplicate address detection (DAD) and the actual address to use for communication.The node then creates a dummy message with the source address of the temporary IP that inquires whether the address is used by any other and floods it to the network.If there is no reply during a given period, the node will consider that it is free and thus will take the address as its own address.Otherwise, it selects another address and iterates the previous procedures again until any free address is found.
In the token-based scheme, a special node is assigned to a token holder, which takes in charge of address allocation for a new node [15].Similar to the centralized scheme, a new node contacts the token holder to get a unique address.However, every node in the network should keep track of the latest address of the holder.

Routing methods
Current routing protocols for WSNs can be grouped into two categories: flat routing [6][7][8] and hierarchical routing [9,10].The flat routing assumes that every node runs the same communication strategy and collaborates the forwarding of data packets toward a sink node with other nodes.In this routing, there is no discrimination on the routing role among sensors.The hierarchical routing, however, imposes a special mission on specially chosen nodes (i.e., cluster headers).Cluster headers collect newly generated packets from noncluster header nodes, aggregate them, and forward them to a sink node.To do so, the cluster headers operate continuously with no idle time, thus consuming more energy than ordinary nodes.
Directed diffusion is a new paradigm that shifted our attention from node-centric routing to data-centric routing [6]. Figure 1 illustrates the schematic view of its three steps.First, a sink node sends its interest to sensors, using flooding (interest propagation).Next, every intermediate node sets up communication paths from a source to a sink, allowing multiple paths (gradients setup).Finally, an optimal path such as lowest-delay path among the multiple paths is chosen to deliver data efficiently (reinforcement).
Energy-aware routing aimed to increase the survivability of networks [8].The basic idea is that it maintains multiple paths from a source to a sink and uses one path among them randomly and probabilistically.It is similar to directed diffusion in that they both construct multiple paths.But unlike the directed diffusion that sends multiple copies of a message on different paths at a time, it only uses a single path  at a time.Every path is assigned a probability to be chosen and it should be evaluated continuously to reflect current link condition.LEACH [9] is the most popular among existing hierarchical routing protocols.It is a self-organizing and adaptive clustering protocol.In LEACH, once a cluster is formed, one of nodes in the cluster is periodically elected as a cluster header randomly and probabilistically to shred energy load among the nodes evenly.Then, the chosen cluster header aggregates the data packets sent from its member nodes and transmits the compressed packets to a sink node.
Lindsey and Raghavendra suggested an optimized version of LEACH called PEGASIS [10].The authors reported that it achieves up to three times more energy reduction than LEACH protocol.Their idea is that it builds a single chain that connects all nodes, where every node is connected to its geographically neighboring node, instead of building multiple clusters for data fusion.Data packets are aggregated over passing one node to another along the chain.And periodically, only one of the nodes in the chain is chosen as a special node that is in charge of final transmission of aggregated data packets to a sink node.To create a chain, the algorithm, however, assumes that all nodes have the global knowledge of the network, which is too optimistic in errorprone wireless networks.

ADDRESSING AND ROUTING FOR ZigBee NETWORK
This section introduces a fully decentralized addressing and routing policy that was adopted as a standard body for early ZigBee products, issues its address wastage problem, and describes several remedies to solve the problem.Recent ZigBee standard, ZigBee Pro by now, claimed that the newest standard could handle thousands of sensors.However, we believe that our proposal, although originally designated for general WSNs, can be immediately applicable to the ZigBee network with a better use that supports tens of thousands of sensor nodes.A device, working as a coordinator or a router, should have a priori knowledge on three network configuration parameters before assigning an address: the maximum number of children that a parent may have (Cm), the maximum depth in the network (Lm), and the maximum number of routers that a parent may have as children (R m ).The interval of the distributed address of a given node depth in a tree is computed by The newly assigned address of an nth child node is calculated by where R n is the nth router, A parent is the address of one's parent, A n is the address of the nth child node of A parent , and d is the node depth.Figure 2 shows an example of addressing assignment, where C m is 4, R m is 4, and Lm is 3. Table 1 presents the intervals per depth for the same configuration parameters.
Typically, a coordinator and routers maintain a routing table to quickly find a route path.In the Cskip-based ZigBee network, a routing path can also be computationally obtained without looking up the table, using (3).When a router receives a data packet, it extracts its destination address to examine whether the destination address exists between the router's address and its maximal address scope as shown in where A r is the address of a router and D is the destination address.
If the condition holds true, the router will transmit the packet to a corresponding child until the final destination node is discovered.Otherwise, it would send the packet to its parent and repeat these procedures.
ZigBee address assignment scheme is the hierarchical addressing architecture.Under this scheme, a parent allocates a segment of its own address space to a newly joining child in a network.A special node, called ZigBee coordinator (ZC), which starts the network, initially owns the whole address space.As new nodes join the network, ZC allocates chunks of address space to the new nodes.Since C m is a given, fixed configuration parameter, it is possible to systematically determine the segment of address space that will be allocated to a new node.Therefore, it will also be acceptable for a parent (including ZC) to have grandchildren before the address segment reserved for its children is used up.In other words, the underlying network tree may not be necessarily a symmetric one.That, in fact, causes a problem.While ZigBee address assignment scheme is very efficient in that it has a fully distributed and reliable mechanism that imposes a very low overhead cost, it has a static nature, thus being very inflexible.As a result, it wastes chunks of address space if the geographical location of sensor nodes is rather skewed.For example, a node that already used up the address segment cannot accept a new joining node, even though a chunk of free addresses is still available for other nodes that are out of communication range of the new node.This address wastage problem has become a widely known problem [2,4,5].
Bhatti and Yue proposed an n-dimensional subspace representation for a given address space [4].It is designed to provide full utilization of available address space.When a new node joins the network, it obtains a unique address from unused space, by navigating a least used dimensional axis.Therefore, any node in the network can have up to n children.Figure 3 demonstrates how to allocate a new address in a two-dimensional space.A network started at the originthat is, (0, 0) in Figure 3-and can grow in any direction that is mostly suited to a physical distribution.The range of address values needs not be the same and depends on how many bits are allocated to each address dimension.If a given address consists of 16 bits and is partitioned equally, every dimension will have the range of 0 and 255.Similarly, two address dimensions may be arbitrarily allocated-say, 10 bits for x-axis and 6 bits for y-axis.In that case, x values range from 0 to 1023 while y value from 0 to 63.
Jeon suggests a simple address assignment and update strategy [5].It assumes that every router (and the coordinator) stores the last address assigned (LAS).This value is the address number that has been lastly used.Once used by any node, its use event will be propagated to all the other routers through a flooding-like mechanism over a given tree topology to make the value consistent.As shown in Figure 4, Coordinator address Assigned address Unassigned address a node A initiates the creation of a new ZigBee network by assigning itself as a coordinator.Thus, its LAS will be 0. As nodes B, C, and D join the network, the node A assigns 2, 3, and 4 as their address, respectively, and updates the LAA value to 5. The LAA values of B, C, D will then be accordingly updated.When a node E joins, it may contact B. B will look up its LAA value, immediately assign the address of E as the value plus one, and inform the use event to all the others.In this way, this address scheme can fully utilize all available address space.When nodes B and D are routing, they use a separate routing table that stores their children addresses.Figure 4 shows that when nodes B and D receive a data packet, they look up its destination address in their table.If the destination node is found, the routers will transmit the data packet to the destination.Otherwise, it will send the packet to a parent node.However, this scheme is not scalable, since the separate routing table will grow proportionally as network size grows.ZigBee Pro, the most recent standard of ZigBee network, standardized a new addressing scheme called stochastic addressing [2].When a new device joins the network, it randomly picks up a valid address.In a 16-bit address space and the network size of a few thousands, it is very unlikely to suffer from frequent address collisions.Moreover, address conflicts are also easily detectable at MAC layer and corrected Certain network topologies exceed maximum tree depth and run out of addresses on branches Stochastic addressing assigns addresses randomly, avoiding topology constrains on network deployments Figure 5: Tree-based addressing and stochastic addressing [5].
with minimal impact to the network.Its first deployments reported that this new standard could handle thousands of devices in an Asian metering product [2].

N-DIMENSIONAL ADDRESSING SCHEME AND ITS ROUTING ALGORITHM
In this section, we introduce a new addressing assignment scheme and its tree-based routing algorithm, TRAACS.

Address assignment by using coordinate system (AACS)
It is designed to support a full utilization of available addressing space without losing any addresses.To achieve this goal, we propose the n-dimensional partitioning of the space.Our partitioning approach, while similar to that of ASAS in terms of space partitioning, is different in that we purposely reserve higher partitions for assigning router nodes.
For example, 16-bit address space may be divided into two subspaces, where first unsigned 8 bits are assigned for x-axis while the latter unsigned 8 bits for y-axis-that is, a single address space is expressed as (x, y) in two-dimensional coordinate system.In a two-dimensional AASC algorithm, the x-axis value refers to the router number on a tree-based routing network and the y-axis value corresponds to the node number of a regular sensor node that is connected to the router whose number is specified in the x-axis.Figure 1 illustrates typical example of our addressing scheme.
As shown in this figure, a newly entered node, if there is no response from other nodes, determines that there is no available node, thus initializing a new network by assigning itself as a coordinator node.Especially, (0, 0) is assumed to be reserved for a coordinator node.When sensors join a ZigBee network, they are classified as either a full function device (FDD) or reduced function device (RFD).If a sensor node is an FFD, it can perform routing function; its address value will be set to (x, 0), where x is a nonzero value.Otherwise, it will not work as a routing node.Its address will have

Router
Sensor node Using this strategy, any given address space can be guaranteed fully utilized when sensors are deployed in real-world environments.
One of disadvantages of 2D partitioning, however, is that any router may not hold as many children as proposed, since sensor nodes tend to be connected to a geographically nearby router.In such heavily skewed distributions of the sensor nodes, the 2D partitioning will be ineffective.To overcome this problem, we extend our original 2D subspacing to a three-dimensional subspacing.A 3D partition remaps the 2D space into three subspaces along x, y, and z-axis.For example, 16 bit address space can be divided into 8 bits, 4 bits, and remaining 4 bits for x-, y-, and z-axis, respectively.Figure 7 illustrates the best possible addressing assignment scheme of our 3D AACS method for ZigBee 16-bit addressing scheme.
(0, 0, 0) 0 (0, 1, 0) 16 (0, 15, 0) 240 (0, 0, 1) 1 (0, 0, 2) 2 (0, 0, 15) 15  As exemplified in Figure 7, a coordinator node starts the address of (0, 0, 0).When a new FFD A is going to be attached to the coordinator, its address will be allocated to (0, 1, 0), meaning that it is the first router that is directly connected to the coordinator.If another FFD B enters into the network, it will be attached to A horizontally and its address will then be (0, 2, 0).Similarly, any FFD whose address is (0, i, 0) will be attached to its previously attached FFD (0, i − 1, 0), where i is in the range of 1 and 15, recursively.After consuming all the bits in y-axis, a newly joined FFD will be attached to the coordinator vertically rather than horizontally; its address thus becomes (1, 0, 0).Next FFDs (1, i, 0) will again be connected to their previous FFDs (1, i − 1, 0).To identify such different assignment procedures, we call routers that use horizontal attachment as subrouter, and the ones that use vertical attachment as root router.Consequently, the coordinator may well be viewed as a special root router of its subrouters whose addresses are (0, 1, 0), . . ., (0, 15, 0).A newly incoming regular sensor node whose address starts from (0, 0, 1) will be attached to a router who has an empty slot for a child.Availability of routers is examined from a root router to its subrouters.We can generalize above intuition for any sensor node (x, y, z).It is expected that the sensor node is the zth child of a subrouter (x, y, 0).If y equals to zero, it will then be the zth child of a root router (x, 0, 0).If x also equals to zero, it will finally be directly connected to the coordinator node (0, 0, 0).In the example shown in Figure 7, a single ZigBee network may have one coordinator and 255 root routers; each of them can have 15 subrouters; and every subrouter can host up to 15 regular sensor nodes.
Our 3D AACS address scheme can be extended to a generic addressing scheme for WSN by varying the bit lengths of each dimension.Assume that a given address length (x + y + z) is partitioned into x bits, y bits, and z bits, where x bits are assigned for root routers, y bits for subrouters, and z bits for ordinary sensor nodes.From this assumption, the maximum numbers of sensor nodes are computed as follows: 2 x − 1: the number of the root router; 2 x × 2 y − 1 : the number of the subrouter; 2 x × 2 y × 2 z − 1 : the number of the sensor node.( For example, in a 12-bit network address space and four bits reserved for each dimension, the number of possible root routers, subrouters, and regular sensor device is 2 4 − 1 = 15: the number of the root router; 2 4 × 2 4 − 1 = 240: the number of the subrouter; 2 4 ×2 4 × 2 4 −1 =3840: the number of the sensor node. ( Our scheme allows network administrators to reconfigure bit lengths for every dimension, depending on their different requirements.

Tree-based routing algorithm, TRAACS
Let a source node, say S, send a message to a destination node, say D. The message is assumed to encapsulate the source address and the destination address at its header.S sends the message to its parent node.The parent node reads the message header to extract the destination address whether it matches any of its children.If so, the parent router will simply deliver the message packet to a designated child node and terminate message routing.Otherwise, it would reroute the message to its parent node (upward) or its child routing node (downward) until the message is finally reached to D. Typically, routers maintain a small memory footprint that stores the addresses of its children that are used during a message routing.In general, smaller number of children takes lesser time for the matching operation.If a routing table size is growing bigger (meaning that a router hosts more children), memory size will accordingly grow.Consequently, the matching operation becomes more crucial for timecritical operations.The existing ZigBee standard avoids this possible performance degradation by adopting Cskip algorithm.It eliminates the iterative matching operations, since a simple computation tells whether a given address is inside a router's address scope.Besides, the router does not require any memory space, because matching operations are no longer necessary.As explained earlier, the Cskip approach, unfortunately, spends the actual address space by assigning addresses in a dispersed manner.
Our AACS algorithm tackles address wastage problem while achieving no memory requirements by eliminating the matching operations.In our addressing scheme, endnodes can only communicate with their parent node that has routing capability.Such hierarchical nature can easily be applied to a tree-based routing.In this section, we will detail the operation scenario for our tree-based routing.We illustrate the case of 2D AACS scheme and later cover the case for 3D scheme.
Suppose that a network is configured to be addressable by 16 bits and our 2D AACS scheme is being used.A router node, during a tree routing, examines the x-axis value of a destination address inside a message packet.If the value is the same as its x-value, it will forward the packet to one of its children, since the destination host is one of its children.Otherwise, it send the message to upward router if the xvalue is less than that of the router or to a downward router until the x-value matches that of a router.Figure 8 shows the example routing path of a message whose source and destination addresses are (3, 3) and (0, 2), respectively.The source node (3, 3) creates a message that should be sent to the destination node (0, 2).The source first sends the message to its parent (3, 0).The parent then compares its own x-axis value with that of the destination.Since its value is larger than that of the destination, it forwards the message to its parent (2, 0).Again, the parent (2, 0) compares the x value and forwards the message to its parent (1, 0).Since its x value is still greater than, it relays the packet to a coordinator (0, 0).Finally, the coordinator recognizes that the given destination address belongs to its address scope and broadcasts the packet to its children.The destination node (0, 2) upon a reception of the message sends back an ACK message to the coordinator to confirm that it successfully receives the packet.This feedback message will (0, 0) 0  eventually reach to the source node by traversing the routing path in an opposite direction.Similar routing procedures can be easily adapted to a 3D AACS addressing scheme.A 3D AACS-based tree routing algorithm is slightly different in that a root router compares the x-axis value of a destination node with its x-axis value while a subrouter compares the x-axis value (and the y-axis value if necessary) of the destination node with its own corresponding axis value.Figure 9 shows another sample case of routing a message from (0, 1, 15) to (2,15,0).A source node transmits a newly created message to its subrouter (0, 1, 0).If a source node is in the form of (x, 0, z), it send the message to the coordinator or its root router directly without traveling through subrouters.The subrouter (0, 1, 0) then compares its x-axis value with that of the destination host.Since no match is detected, it sends the message to the coordinator.The coordinator forwards the message to its child root router, which will constant to relay the message to a child root router until the same x-axis valued root router is contacted.Once the message is routed to a root router (2, 0, 0), it is then again delivered to its subrouter (2, 1, 0).The subrouter (2, 1, 0) compares x-axis values first and then compares The location-aware routing algorithms perform routing operations under the assumption that sensor nodes know the locations of other nodes a priori.To detect their own location, the sensor devices may be equipped with positioning devices such as GPS.Many location-aware routing algorithms, however, typically require a sensor node to be aware of the location of other nodes to talk with.To do so, a sensor node continues to talk to a server database to notify its location update periodically and to resolve the location of other nodes, which is a rather expensive approach.If relaxing the assumption that we do not need to know the exact location of a destination node for communication purpose, we may take advantage of using the proximity table that has already been widely studied in many distributed environments.
To begin, let us assume an AACS-enabled ZigBee network.When a new node joins the network, it obtains a unique address by attaching to its parent node.Only by communicating with the parent node, it can resolve all the addresses of currently available nodes.Therefore, the location-based routing algorithm can be applied without installing any additional resources.Figure 10 exemplifies an irregular ZigBee network, whose addressing scheme is based on our 3D AACS.This irregular network is formed by the coordination of (0, 0, 0).Every sensor address is uniquely assigned by the combination of join order and response order from candidate parent nodes.
If a router node is allowed to cache neighboring nodes in a proximity routing table and maintain them by their closeness to it, a suboptimal location-aware routing can be achievable.For example, a router (1, 1, 0) stores geographically neighboring router nodes such as (1, 2, 0), (1, 0, 0), (2, 0, 0), (0, 0, 0), (0, 1, 0), and (0, 2, 0) in the proximity-based routing table.Instead of performing tree-based routing, routers may route to an alternative path that is aware of geographical closeness.Location-aware node selection scans the routing addresses in the proximity tables, computes their distances to the destination, chooses the minimal node, and then forwards a message to the node.Since the node selection is done at the router level, we only assume to use x-and yaxis values while ignoring z-values.In addition, we prefer selecting the nodes that are the closest x-axis value to the destination first.If multiple nodes are retrieved, we will refine the selection by choosing the closest y-axis node.
This selection strategy guarantees to reach to the final destination without any looping, since resulting distance to the destination always decreases as visited hop counts are increased.However, it does not guarantee the optimality.It is because, in some cases, a routing path should be inevitably rolled back to complete the routing.As a result, the locationaware routing algorithm works well only in well-spaced sensor distributions.
Our simulation shows that address allocation and routing of sensor network very deeply consider network efficiency.To consider this matter, the main purpose of the effective address assignment and routing is to minimize the average energy consumption of each node in the network.Since each node has limited energy, the effectiveness of the sensor network is assessed by the efficiency of the energy consumption.The most influential element for this energy consumption is the average number of the multihops in the sensor network.The number of the multihops means the number of the router nodes which the packets made in the source nodes send by to be delivered to the destination node.Considering this point, if there are many routers for the packets to pass by on the way to the destination, the packets should go through the lower source nodes.In the event, the totality sensor network system increase energy consumption of the relevant source nodes as well as that of the router nodes.This is the reason that the less the average number of the multihops from the source nodes to the destination node, the longer the durability of the network due to the reduced energy consumption.Of course, there are other parameters that should be considered in terms of energy consumption such as end to end delay, packet delivery rate, routing overhead, and so forth.And yet these parameters are also significantly influenced by the average number of the multihops in the sensor network.For example, the less the average number of the multihops, the shorter the end to end delay, that is, the delayed time between each node due to the reduction of the traffic in the sensor network.In terms of packet delivery rate, the more the hops that the packets generated in the source nodes should go through the way to the destination node, the higher the possibility that the packets drop.Therefore, higher average number of multihops means the lower packet delivery rate.In terms of routing overhead, the increasing average number of the multihops is expected to bring about the network overload due to the increase in the number of packets treated inside the network.Without operating a simulation for the demonstration, it is anticipated that the smaller the number of multihops is, the shorter the end to end delay is, the higher the packet delivery rate is, and the smaller the routing overhead is.
For the average number of the multihops considerably influences on other parameters, it seems sufficient to simulate only the average number of the multihops in order to discuss the efficiency of the sensor network and the validity of the address assignment methods which decided the network efficiency.

CONCLUSIONS AND FUTURE DIRECTION
In this study, we have investigated the problem of existing addressing schemes and their routing algorithms by exemplifying the case of ZigBee network.In particular, we have concentrated on our discussion on the wastage of address space.To overcome this problem, we have proposed a three-dimensional addressing scheme by mapping a single address space into a three-dimensional coordinate space.Another benefit of this scheme is that it does not require any additional routing memory space, since it uses an implicit tree-based routing algorithm.Moreover, it can save a lot of energy by shortening the average hop count during a routing.Compared with legacy ZigBee standard, our new addressing and routing scheme reported two times lesser average hop count for a larger network.
Next research should study an area of applying the ZigBee sensor network.Also, it should generalize this algorithm which is to be applied by the other sensor networks.

Figure 3 :Figure 4 :
Figure 3: Illustration of incremental address assignment in a twodimensional subspace partitioning.

Figure 6 :
Figure 6: Best possible addressing configuration of our two-dimensional scheme.

Figure 7 :
Figure 7: Illustration of address assignments for three-dimensional AACS approach.

Figure 8 :
Figure 8: A sample example of a tree-based routing under 2D AACS scheme in a 16-bit network.

Figure 12 :
Figure 12: Several network topologies assigned by individual address assignment algorithms.

Figure 13 :
Figure 13: The average hop counts as a function of network size.

Table 2 :
The numbers of MHN of different topologies as a function of network size.